Secret Societies and the underground are the only way we're going to allow for this.
Sending messages without revealing the sender is just the perfect setup for trolling and griefing.
There exists sending messages where you just need to bribe the scribes from revealing, who you send to.
If your character want engage in secret society ways, I accepted Anaris explanation. People can plot rebellions and what-not.
Now your last part, anonymous love letter intrigued me
